Weak-field limit of conformal Weyl gravity

TL;DR

This paper investigates the weak-field limit of conformal Weyl gravity as an alternative to General Relativity, finding it incompatible with Solar System observations due to its predictions.

Contribution

It provides the first detailed weak-field solutions of conformal Weyl gravity for arbitrary static matter distributions and tests their observational viability.

Findings

The theory's predictions do not match Solar System data.

Conformal Weyl gravity cannot replace General Relativity at weak-field scales.

The solutions highlight fundamental inconsistencies with established observations.

Abstract

We study the weak-field limit of the conformal Weyl gravity suggested by Mannheim as an alternative to Einstein's General Relativity modeling both dark matter and dark energy. We solve the field equations of the theory in the weak-field approximation for an arbitrary spherically symmetric static distribution of matter in the physical gauge with constant scalar field. Analysing the obtained solution, we conclude that the conformal theory of gravitaty is inconsistent with the Solar-system observational data.